# Using the pythagorean theorem, solve for a:  `c =` `sqrt(a^2 + b^2)`

lemjay | High School Teacher | (Level 2) Senior Educator

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`c=sqrt(a^2+b^2)`

To solve for a, the square root must be eliminated. To do so, perform its opposite operation. So, square both sides of the equation.

`c^2=(sqrt(a^2+b^2))^2`

`c^2=a^2+b^2`

Next, move b^2 to the other side to have a^2 only at the right side. Again, do the opposite operation. Since the operation between a^2 and b^2 is addition,  then subtract both sides by b^2.

`c^2-b^2=a^2+b^2-b^2`

`c^2-b^2=a^2`

And to have a only at the right side, its exponent 2 must be removed So, take the square root of both sides of the equation. And as per square root property, a has two values, the positive and negative. So,

`+-sqrt(c^2-b^2)=sqrt(a^2)`

`+-sqrt(c^2-b^2)=a`

Note that if a represents a dimension of a figure, take only the positive expression.

Since the problem does not indicate what a represents for, then consider the two expression of a.

Hence, `a= +sqrt(c^2-b^2) `   and   `a=-sqrt(c^2-b^2)` .